Over the past years, fluorescence microscopy (FM) has steadily progressed in increasing the localization precision of fluorescent emitters in biological samples and led to new claims, whose rigorous validation remains an outstanding problem. We present a novel, to the best of our knowledge, multi-parameter estimation framework that captures the full complexity of a single-emitter FM localization experiment. We showcase our method with Minimum Flux (MINFLUX) microscopy, among the highest-resolution approaches, demonstrating that (i) the localization precision can be increased only by turning the illumination intensity up, thus increasing the risk of photo-bleaching, and it is independent from the beams' separation, and (ii) in presence of background noise, the localization precision decreases with the beams' separation. Finally, we apply our method to Minimum Flux Stimulated Emission Depletion (MINSTED) microscopy, showing that a reduction of the beam width can provide similar performance to MINFLUX.
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